Abstract

A newly defined notion of convex closedness regarding a set is used in order to state a necessary and sufficient criterion for the min-sup property in non necessarily convex primal-dual optimization problems, generalizing well-known theorems valid in the convex setting. Our main result is then applied to the classical penalty method.

Author information

Contact details are reproduced from the original publication and may be historical.

Emil Ernst

Université Aix Marseille, Centrale Marseille, I2M – UMR 7373, 13453 Marseille, France and: CNRS

Emil.Ernst@univ-amu.fr

Keywords

  • Dual optimization
  • min-sup property
  • convex closedness regarding a set
  • penalty method

Mathematics Subject Classification

49M30, 49N15, 52A20

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Suggested citation

E. Ernst, M. Volle. “Zero Duality Gap and Attainment with Possibly Non-Convex Data.” Journal of Convex Analysis 23 (2016), No. 2, 615–629. https://doi.org/10.68381/jca23023

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Published by Heldermann Verlag, 2016. Rights now held by Banach Press LLC.